We were discussing the “Elongation of uniformly tapering circular rod” and “Elongation of uniformly tapering rectangular rod” and also we have seen “Stress analysis of bars of composite sections” and “Stress analysis of bars of varying sections” with the help of previous posts.

Now we are going further to start our discussion to
understand the concept of “Thermal stress in composite bar”, in subject of
strength of material, with the help of this post. We have already discussed the
basics of thermal stress and strain and we will use that concept here too.

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**Let us see here ****the concept of thermal stress in
composite bar**

First we will understand here, what is a
composite bar?

Composite
bar is basically defined as the bar made by
two or more than two bars of similar length but different materials and rigidly
fixed with each other in such a way that it behaves as one unit and strain
together against external load i.e. it behaves as single unit for compression
and extension against compressive and tensile load.

We can say here from the definition of
composite bar that strains will be same for each bar of composite bar and hence
actual change in length will be similar for each bar or we can say that actual
strain will be same for each bar of composite bar and we will use this concept
during thermal stress analysis for composite bars.

Let us consider that we have one
composite bar consisting two bars of different materials i.e. one bar of brass
and other bar of steel and it is displayed here in following figure. Let us
assume that we are now going to heat the composite bars up to some temperature,
so what will be expected to occur?

As we know that if we are going to heat any
material, there will be increase in temperature of the material and hence there
will be increase in dimensions of the material. Similarly if we are going to
cool the material, there will be decrease in temperature of the material and
hence there will be decrease in dimensions of the material.

We can simply say that there will be free expansion or free contraction in the material according to the rising or lowering of temperature of the material. If free expansion or free contraction of the material due to change in temperature is restricted partially or completely, there will be stress induced in the material and this stress will be termed as thermal stress.

We must note it here that if free expansion or free
contraction of the material due to change in temperature is not restricted i.e.
expansion or contraction of the material is allowed, there will no stress
developed in the material.

Now suppose if brass and steel both are not in
composite in nature and we want figuring out the change in dimensions separately
for steel and brass due to change in temperature, we will be able to say easily
that change in length of the brass bar will be more than the change in length
of the steel bar for similar rise in temperature of the bar and this is
basically due to different co-efficient of linear expansion i.e. α for brass and
steel.

Co-efficient of linear expansion i.e. α for brass will be more than as
compared to steel and therefore change in length of the brass bar will be more
than the change in length of the steel bar for similar rise in temperature of
the bar.

But in this situation, brass and steel are in composite state and therefore both members of composite bars will not be able to expand freely. Hence the expansion of the composite bar, as a whole, will be less than that for brass but more than that for steel.

We must have to note it here that brass will be
subjected with compressive load or compressive stress because steel will
restrict the brass to expand up to the limit up to which brass could be
expanded.

And similarly, steel will be subjected with tensile load
or tensile stress because brass will force the steel to expand beyond the limit
up to which steel could be expanded. In simple words, we can say that both
members of composite bars will be under stress but one will be in tensile
stress and other will be in compressive stress i.e. steel will be under tensile
stress and brass will be under compressive stress.

Do you
have any suggestions? Please write in comment box

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**Reference:**

Strength of material, By R. K. Bansal

Image Courtesy: Google

We will see another important topic, in the category
of strength of material, in our next post.

Procedure of finding thermal stress in a composite bar i want w8ll you make it

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